Question

Find the coordinates of the point which divide the line segment joining A
(-2,2) and B(2,8) into 4 equal parts.​

Answer 1

Answer:

The coordinates of points which divide the line segment AB are P ≡ ($-1 , \frac{7}{2}$), Q ≡ ($0 , 5$) and R ≡ ($1 , \frac{13}{2}$).

Step-by-step explanation:

Given points are A(-2,2) and B(2,8). Let points which divide line segment AB into 4 equal parts be P(divides AB in ratio 1:3), Q(divides AB in ratio 2:2) and R(divides AB in ratio 3:1).

w.k.t, the co-ordinates of point which divide a line segment joining two points (x₁,y₁) and (x₂,y₂) in the ratio m:n are ≡ ($\frac{mx_{2}+nx_{1}}{m+n} , \frac{my_{2}+ny_{1}}{m+n}$).

⇒ Co-ordinates of point P = ($\frac{1.2+3.(-2)}{1+3} , \frac{1.8+3.2}{1+3}$) = ($\frac{2-6}{4} , \frac{8+6}{4}$)

or P ≡ ($-1 , \frac{7}{2}$)

⇒ Co-ordinates of point Q = ($\frac{2.2+2.(-2)}{2+2} , \frac{2.8+2.2}{2+2}$) = ($\frac{4-4}{4} , \frac{16+4}{4}$)

or Q ≡ ($0 , 5$)

⇒ Co-ordinates of point R = ($\frac{3.2+1.(-2)}{3+1} , \frac{3.8+1.2}{3+1}$) = ($\frac{6-2}{4} , \frac{24+2}{4}$)

or R ≡ ($1 , \frac{13}{2}$)

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